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arXiv · 2606.13933

More Residually Solvable One-Relator Groups

Lucy Koch-Hyde·Siobhan O'Connor·Eamonn Olive
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Abstract

We say a word in a free group is ``partially positive'' if there is at least one generator which appears in the word, but does not appear with negative exponent. We show that one-relator groups with a partially positive relator are residually solvable. This extends a theorem of Baumslag showing one-relator groups with positive relators are residually solvable.

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Lucy Koch-Hyde, Siobhan O'Connor, Eamonn Olive. 2026-06-11. More Residually Solvable One-Relator Groups. https://arxiv.org/abs/2606.13933

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